QPR was one of the 1st in England I think. That was in the 80's. The FA banned them in 88.
But the first in Europe was apparently in Italy in 1970:
FLORENCE, Italy, Sept. 22 (Reuters)
Work began here today on laying Europe's first artificial soccer pitch, the Italian Football Federation announced.
The pitch of 'Tartan Turf' which is commonly used for athletics tracks, is being prepared at the Coverciano ground at the Federation's Florence headquarters.
A spokesman said today that as yet there were no plans for holding matches on the new field.
He added that the scheme, which is being financed by the League, the Italian Olympic Committee and the manufactures of the artificial turf was purely experimental.